{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solving a simple differential equation\n",
    "\n",
    "---\n",
    "\n",
    "This notebook illustrates how to solve a simple differential equation using [Julia's ODE library](https://github.com/JuliaLang/ODE.jl).\n",
    "\n",
    "The equation $ x''(t) + x(t) = 0 $ has as possible solution $ x(t) = sin(t) $\n",
    "\n",
    "Let's see how we can set this up so that it can be solved numerically.\n",
    "\n",
    "---\n",
    "\n",
    "Let's start by importing ODE:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "using ODE;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to define the system of differential equations as an equation of the form: ${\\bf y}' = {\\bf f}(t, {\\bf y})$,  where ${\\bf f}(t, {\\bf r})$ is the mapping function that given a time $t$ and the current value of ${\\bf y}(t)$ gives us its derivative.\n",
    "\n",
    "We are writing ${\\bf f}$ and  ${\\bf y}$ in bold because they can actually be vectores. This is useful if you want to solve a higher order differential equation, representing it as a system of equations.\n",
    "\n",
    "----\n",
    "\n",
    "So, the equation:\n",
    "\n",
    "$$ x''(t) + x(t) = 0 $$\n",
    "\n",
    "can be expressed as a system of first order differential equations:\n",
    "\n",
    "$$ \\begin{cases} \n",
    "  x'(t) = v(t) \n",
    "  \\\\\\\\ \n",
    "  v'(t) = -x(t)\n",
    "\\end{cases} $$\n",
    "\n",
    "So, let's encode the function ${\\bf y}' = {\\bf f}(t, {\\bf y})$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "function f(t, y)\n",
    "    # Extract the components of the y vector\n",
    "    (x, v) = y\n",
    "    \n",
    "    # Our system of differential equations\n",
    "    x_prime = v\n",
    "    v_prime = -x\n",
    "    \n",
    "    # Return the derivatives as a vector\n",
    "    [x_prime; v_prime]\n",
    "end;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, to solve this numerically, we just need to setup the initial conditions (i.e., $x(0)$ and $x'(0)$) and a time span to simulate. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Initial condtions -- x(0) and x'(0)\n",
    "const starty = [0.0; 0.1]\n",
    "\n",
    "# Time vector going from 0 to 2*PI in 0.01 increments\n",
    "time = 0:0.1:4*pi;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's simulate. The ode45() function will return a time vector and the $y$ vector solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "t, y = ode45(f, starty, time);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's extract $x(t)$ and $x'(t)$ from ${\\bf y}$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = map(y -> y[1], y)\n",
    "v = map(y -> y[2], y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now, let's plot it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x31ed6bb50>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "using PyPlot\n",
    "plot(t, x, label=\"x(t)\")\n",
    "plot(t, v, label=\"x'(t)\")\n",
    "legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's it."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 0.4.3",
   "language": "julia",
   "name": "julia-0.4"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "0.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
